Probability

Probability Probability can be defined as the chance of an event occurring. It can be used to quantify what the “odds” are that a specific event will occur. Examples of how probability is used everyday would be weather forecasting, “75% chance of snow” or for setting insurance rates. Bluman, Chapter 4

Sample Spaces and Probability A probability experiment is a chance process that leads to well-defined results called outcomes. An outcome is the result of a single trial of a probability experiment. A sample space is the set of all possible outcomes of a probability experiment. An event consists of outcomes. Bluman, Chapter 4

Sample Spaces Experiment Sample Space Toss a coin Head, Tail Roll a die 1, 2, 3, 4, 5, 6 Answer a true/false True, False question Toss two coins HH, HT, TH, TT Bluman, Chapter 4

Example 4-1: Rolling Dice Find the sample space for rolling two dice. Bluman, Chapter 4

A sum less than or equal to 4 Example #1 If two dice are rolled one time, find the probability of getting these results. A sum of 6 Doubles A sum of 7 or 11 A sum greater than 9 A sum less than or equal to 4

A sum of 6 Total of 36 outcomes Doubles There are six ways to get doubles. They are (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6).

Total of 36 outcomes A sum of 7 or 11 There are six ways to get a sum of 7. They are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). There are two ways to get a sum of 11. They are (5,6) and (6,5). A sum of greater than 9 To get a sum greater than nine, one must roll a 10, 11, or 12. There are six ways to get a 10, 11, or 12. They are (4,6), (5,5), (6,4), (6,5), (5,6), and (6,6).

Number of Tests Performed e. The patient has had 1 or 2 tests done. Number of Tests Performed Number of Patients 12 1 8 2 3 4 or more 5